You are correct that 12 volts is not high voltage. However it can still heat up a ring or watch in milliseconds if the power supply can supply the needed amperage.
Using the equation V (volts) * I (Amps) = P (watts) we could calculate the power of putting a car battery through a ring: 12 volts * 100 amps[1] = 1200 watts. That's more than your average microwave.
The reason you don't heat up when you touch a car battery is that at 12 volts your skin (mostly an insulator) won't conduct the needed amps. Metal (a conductor) will however transfer close to the full 100 amps of the battery.
With 110/220V AC, you only need to touch the phase to be in trouble. With 12V, your body will basically block all current from flowing, so to get in trouble you'll need to accidentally make the metal part to connect both electrodes of the battery (short circuit). This is much, much less likely than with other low voltage system (btw, 12V is Extra-low voltage).
One of the elecrodes of the battery (-) is generally connected to the metal body. You only need a cable touching your ring while your hand rests on the frame to cause a short, which can happen. Or a loose cable touching the car frame.
It's generally immediately obvious, and can be remediated by pulling the cable away before it welds. But dropping a screwdriver in the wrong place can and will (statistically, thanks murphy) happen, so better use insulated screwdrivers and gloves, to reduce the likeliness of it happening.
> One of the elecrodes of the battery (-) is generally connected to the metal body. You only need a cable touching your ring while your hand rests on the frame to cause a short
The current won't flow through your hand, 12V is too low to pass your skin with a significant current. The only way the ring can have raise to a significant heat is if the ring itself touches both sides of the circuit (anode -> car frame -> ring -> wire -> cathode). Anode -> car frame -> hand -> ring -> wire -> cathode won't cause any short, because your hand acts as a big resistance in that circuit.
> 12V is too low to pass your skin with a significant current
Now of course the human body has a complex impedance, with cell membranes acting as capacitors: higher frequencies let more current flow. And that also depends on how much skin there is (single finger vs arm to foot), if it is wet, etc. I remember trying a (discharged) 9 V battery on my tongue as a kid... that was literally quite a shock, even with continuous current.
In the end, I wouldn't bet that an electrocution is impossible using a mere 12V of electric potential.
We weren't talking about electrocution here, but about heating a ring quickly enough to burn you, which requires a much higher amperage than what's needed to kill you.
Anyway, given that 12V is considered safety voltage for submerged swimming pool material in France, I'm pretty confident it is be extremely unlikely to kill anyone.
Using the equation V (volts) * I (Amps) = P (watts) we could calculate the power of putting a car battery through a ring: 12 volts * 100 amps[1] = 1200 watts. That's more than your average microwave.
The reason you don't heat up when you touch a car battery is that at 12 volts your skin (mostly an insulator) won't conduct the needed amps. Metal (a conductor) will however transfer close to the full 100 amps of the battery.
Here's an example of the effect[2]
[1]: https://www.bestpowerbattery.com/how-many-amps-is-a-car-batt...
[2]: https://www.youtube.com/watch?v=8Wx6-ysokJU